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 Sample Size and Power Calculations

## One-Way ANOVA

The power for the one-way ANOVA is computed in a similar manner as for the hypothesis tests. That is, power is the probability of correctly rejecting the null (all group means are equal) in favor of the alternative hypothesis (at least one group mean is not equal), when the alternative is true. The sample size is the number per group; these calculations assume equally sized groups. To compute the power, you make use of the noncentral F distribution. The formula (O'Brien and Lohr 1984) is given by

where F is distributed as the noncentral and is the () quantile of the F distribution with and degrees of freedom.

is the numerator df

is the denominator df

n
is the number per group

r
is the number of groups

is the noncentrality parameter

is the corrected sum of squares

is the mean of the gth group

is the overall mean

is estimated by the mean squared error (MSE)

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